Transmission line



May l3, 1941. ROQSENSTEIN 2,241,616

TRANSMISSION LINE Filed Dec. 6, 1938 I INPUT OHM/C RES/STANCE I INPUT OHM/C RESISTANCE DETUN/NG INVENTOR HANS O. ROOSENSTE/N BY Wi al ATTORNEY for a wide band of frequencies. the consumer or load resistance is of a complex Patented May 13, 1941 TRANSMISSION LINE.

Hans Otto Roosenstein, Berlin, Germany, assignor to Telefunken Gesellschaft fiir Drahtlose Telegraphic m. b. H., Berlin, Germany, a corporation of Germany Application December 6, 1938, Serial No. 1244,164 In Germany December 1, 1937 4 Claims.

The invention is concerned with an arrangement adapted to couple a radio frequency load or consumer, such as a short-wave antenna, with an energy feeder line or co-axial cable so that, within a wide frequency band the apparent resistance of the consumer or load device will be matched to the charactertstic impedance of the energy feeder under conditions unaffected 'by the frequency. One particular field of application of the basic idea of the invention is in connection with the transmission of television programs, that is, video signals in which, as well known in practice, frequency bands of extremely great width must be fed to an aerial in order to be radiated therefrom. The means and ways adapted to match the load resistance to the surge impedance of the energy feeder which serve to preclude the risk of reflections and thus of standing waves along the line, are found to be no longer serviceable Where very wide frequency bands are concerned, on the ground that they are invariably proportioned to suit a single frequency, with the result that they insure accurate matching only for a single frequency in the band, that is, for the carrier frequency, while for all of the sideban-d be transformed to a constant value correspondfrequencies the antenna is mismatched to some extent. This is conducive to distortion and a substantial impairment of the general fidelity of transmission.

Now, the object of the invention is an arrangement which will insure an optimum matching between the consumer impedance and the energy feeder surge impedance in a uniform way throughout a whole frequency band.

For a better understanding of the invention and its underlying idea, the basic physical condi- Y tions shall first be outlined which will arise in establishing coupling relationship between a line and any consumer or load resistance whatever As a general rule,

nature; hence, it may be conceived to be replaced by or consist of an ohmic resistance and a reactance. If both the ohmic resistance component, as well as the reactance or the wattless component are independent of frequency (though this,

as a general rule, is not true of antennae), the problem which arises is to connect this constant impedance with the predominantly ohmic char-- effective resistance of the consumer or load must similar conditions (that is, unaffected by frequency). Now, one of these two demands as a general rule is readily fulfillable. Thus, the suggestion has been made in the prior art to transform the load reactance by the aid of a suitable length of line inserted between the aerial and the energy feeder line and having a proper surge impedance to a value practically down to zero under conditions largely independent of the frequency. However, what has been overlooked in such a scheme is that also the ohmic resistance of the load undergoes transformation such that the originally frequency independent ohmic resistance has turned out to be affected by frequency. The result is that while matching prevails uniformly throughout the whole frequency band for the reactive component, mismatching has been introduced for the ohmic resistance component for the remoter side band frequencies.

Another fact is that the load reactance and in numerous cases, even the load ohmic resistance, are themselves dependent upon frequency, and in such event the transforming means additionally must have the property of compensating the frequency curve of the load impedance while at the same time fulfilling the above mentioned conditions. Heretofore, this problem has only been solved by expanding the load impedance by additional lumped inductances and capacitances in such a way that what was originally a frequency dependent load reactance was transformed down to zero level independent of the frequency. At the same time ohmic resistance of the load, assumedly independent of frequency, was transformed to a constant value independent of the frequency. However, this still did not afford ways and means to match a load impedance, no matter what its value, to an energy feeder surge impedance also of an arbitrary value, in as much as the transformed value of the transformed load ohmic resistance was fixed by the required transforming properties, and, as a general rule, failed to coincide with the desired energy feeder surge impedance.

Moreover, the supplemental concentrated or lumped inductances and capacitances before referred to and serving for matching are not readily applicable to ultra-short waves, for example, a wave length less than 10 meters, for the reason that they invariably consume a large wattless power with resultant losses and dissipation, while it happens that just with these short waves perfect freedom from losses is imperative because of the difiiculties attendant upon their generation.

According to the invention complete and practically constant matching within a wide frequency band is obtainable by including between the consumer or load and the energy feeder line or coaxial cable two or more transformation lines in series possessing within their lengths a constant surge impedance. The surge impedance values and lengths are so chosen that the load reactance, under conditions independent of the frenquency, is transformed practically down to zero level, while the ohmic or effective resistance of the consumer or loadis transformed to a constant value which agrees with the surge impedance of the energy feeder line. The invention is predicated upon an appreciation of the fact that frequency independent transformation, within a stipulated frequency band, of any impedance to another definite impedance value, preferably a pure ohmic resistance may be accomplished by the connection in series of several transformation lines with dissimilar surge impedances. The transformation lines may be of dissimilar lengths. The use of two transformation lines between an antenna and an energy feeder line, basically speaking, has been known in the prior art, though in that case the two lines serve the purpose of insuring transformation in two distinct stages rather than, as is the customary practice, by means of a single ./4 line. Where the two-stage scheme is used more favorable rules regarding dimensions for the transformation lines result because the resistances to be matched to one another are of widely different values. However, exact matching is assured only for a single frequency value just as in the case of the conventional ./4 transformation line.

This situation is easily explainable by reference to the fundamental formulae for transformation lines. The surge impedance of the M4 line must be so proportioned that it will be equal to the geometric mean of the two resistances to be matched to each other. As already pointed out, this, in many instances, results in practically non-representable surge impedance values. But if two ./4. lines are connected in series then the condition is that the ratio of their surge impedances is equal to the square root of the ratio of the resistances which are to match each other. There is no stipulation respecting the absolute value of the surge impedances themselves so that these may be given a value most favorable from a constructional viewpoint. However, this arrangement and scheme fails completely in broad band transmission for the reason that the frequency dependence of transformation is, as a rule, extremely great. It is here the invention applies which instructs that not only the ratio between surge impedances, but also the surge impedances themselves should be so chosen that the transformation properties either are entirely independent of the frequency or depend upon frequency in such a way that the frequency dependence of the load impedance is compensated. The fact that such choice of the surge impedances is possible could not be predicted and foreseen, in fact, it is demonstrable only by an extremely close analysis of the line equations.

As can, be readily understood, an extremely great variety of embodiments are conceivable adapted to carry the broad idea of the invention into practice, inasmuch as the lengths and the surge impedances of the different transformation lines may by so widely different manners be matched to one another that the requisite adaptation is realizable. However, the different embodiments are not all equivalent since it is not possible to realize in practice each and every value of a surge impedance since the dimensions governing the surge impedance between the two conductors of a double wire line such as a coaxial cable or line may not be chosen above or below a certain maximum or minimum value. Hence, conditions are restricted to the surge impedances available for the line. Out of a multiplicity of feasible embodiments of the invention those must be selected which will prove most favorable for practical application. In what follows a few of these shall be described and discussed by the aid of numerical examples, and by reference to the accompanying drawing in which Figures 1 and 2 illustrate embodiments of the invention while Figure 3 is a curve illustrating the operation of the embodiments of Figures 1 and 2; and Figure 4 illustrates a further modification of the invention.

If the ohmic resistance of a load is constant and independent of the frequency, while the load reactance has a frequency characteristic as is approximately true for short-wave antennae of ./4 length fed at the base, the transformation of this impedance into a frequency-constant ohmic resistance is obtainable by connecting in series two lines of )./2 length according to Fig. 1. Referring to Figure 1, i denotes a radio frequency transmitter which is connected with an antenna 3 by means of an energy feeder line or In these equations, X0 denotes a reactance resulting from the formula:

where X is the reactance of the antenna and y the detuning, that is w/wow0/w (where mo the resonance frequency of the antenna). In the presence of detuning 11:0, in other words, for the resonance frequency of the antenna the antenna reactance is equal to zero. to; stands for the detuning for which the transformed reactance is exactly equal to zero, and this is predeterminable according to the width of the frequency band to be transmitted. Where normal television bands are involved, yr is best made approximately equal Referring again to the above formula, RA designates the ohmic resistance of the antenna. If in a practical instance the effective or ohmic resistance of the antenna is equal to 25 ohms, the frequency function or characteristic of the antenna reactance y'63 ohms and therefore Xn=63 and yk=.1 then W1 (surge impedance of the first transformation line) "8.65 ohms andWz 43 ohms. The following tabulation will make it clear in what way the impedance of the antenna is transformed by the two transformation lines. In this tabulation y again denotes as above detuning, Rn the transformed ohmic resistance, and Xn the reactance:

y Rn- Xulatter may be so proportioned that its surgeimpedance from the outset is equal to the transformed load resistance. In the numerical example before cited this resistance was 25 ohms, a value which is unfavorable in practice for the normal energy feeder line or coaxial cable. In accordance with the invention it will therefore be expedient to insert additional transformation lines between the transformation lines and the coaxial cable with the result that the load reactance transformed down to zero and independent of frequency will continue being zero and in- This purpose is fulfilled by the seriation of two M4 transformation lines as shown in Figure 2. Referring to this figure, l is the transmitter, 2 the coaxial cable, and T3 and T4 the two M4 transformation lines. The part connected with line T3 is represented in Figure 2 in the form of a terminating resistance R1 which represents a zero load reactance independent of frequency and an ohmic load resistance also independent of frequency but of a value incorrect for direct connection to feeder line 22. It will be evident that the resistance (R1) which may be a result of the polarization of the two M4 lines as discussed with reference to Figure 1 need not necessarily be a load ohmic resistance transformed as in that figure; as a matter of fact this first transformation of the load resistance may be accomplished by some other ways and means such as lumped inductances and capacitances. Also, of course, R1 could consist directly of a load or consumer whose properties correspond to the impedance appearing at the input of the transformation line T2 in Figure 1 which has a frequency independent 'reactance of zero value and a frequency independent constant effective or ohmic resistance.

So far as the transformation lines Ta and T4 in Figure 2 are concerned there holds first good the above mentioned Well known condition that the ratio of the surge impedances is equal to the square root of the ratio of the resistances to be matched to each other. However, as also pointed out above this condition does not yet sufiioe to insure frequency independence of the transformation; Hence, afurther condition must be laid downregarding the absolute values of the surge impedances. As follows from theory, both conditions are fulfilled-by making arrangements so that the ohmic resistance (R1 in Figure 2) appearing at the end of the two transformation lines, the surge impedance W3 of the preceding transformation line T3, the load ohmic resistance R3 of this line, the surge impedance W4 of the next following transformation line T4, and the surge impedance Wk of theenergy feeder line 2 or 4 their values result in a geometric series. In other words, there should be: (5) E=YK =E K L W3 R3 W4 W):

This condition embraces also the fundamentally known demand that:

W. W]. W3 R1 1 Furthermore, the various surge impedances are also fixed as to their absolute values so that as above pointed out frequency independent transformation is assured.

Suppose that in a numerical example R1 equals 25 ohms, Wk=60 ohms, W3=-3-1 ohms and W4=48 ohms. The ensuing relations are illustrated graphically in Figure 3. By the absoissae is here indicated the detuning y in terms of percent, by the ordinates the values of the ohmic resistance appearing at the input of the transformation line T4 in Figure 2 (curve I) as Well as the reactance appearing at the same place (curve II) in terms of ohms. As will be seen, between 0 and 10 percent de'tuning, the reactance is practically equal to zero, and the effective or ohmic resistance equal to 60 ohms, in other words, equal to the surge impedance of the energy feeder line.

By arranging in series two transformation lines as in Figure 1 and two transformation lines as in Figure 2, it is thus feasible to transform the frequency dependent reactance of the antenna to zero independent of the frequency, while the ohmic resistance of the antenna assumed to be independent of the frequency is transformed to a desired value, under conditions independent of frequency, that is to say, to the value of the surge impedance of the coaxial cable. As will thus be seen optimum matching prevails throughout the whole band. As shall be demonstrated in what follows, the identical end is obtainable also by the use of only three transformation lines. With slightly less compensation of frequency dependence of the load reactance, that is, with a. somewhat narrower permissible frequency band the same purpose is realizable even with only two transforation lines.-

Referring to Figure 4, I again denotes the transmitter, 2 is the coaxial cable or feeder line, T1 a transformation line of a length M2, T2 and T3 each a transformation line of M4 length. The consumer or load is indicated by the equivalent diagram comprising for instance, an antenna of M4 length fed at its base end with an ohmic component RA and wattless component X=yXo. Also for this arrangement there holds good first the known condition (7) which with the use of denotations as chosen in Figure 4 assumes this form:

XL D W R small detuning practically undergoes no transformation by the M2 line, itwill be seen that the terminating impedance of the transformation line T2 consists of the ohmic resistance RA of the load and the load reactance transformed by the line T1. With this terminating resistance the optimal absolute values of the surge impedances W2 and W3 suited for broad-band transmission may be determined by which the complex terminating resistance is transformed to the ohmic surge resistance WK of the coaxial cable. 'The surge impedance of transformation line T1 which may be chosen at will is then fixed in such a way that the frequency dependence of the ohmic resistance transformation by this line will be as low as possible. The most favorable value for this surge impedance is as follows:

Suppose that in a concrete case the ohmic resistance of the antenna RA='18 ohms, X=63 ohms and WK=60 ohms. The optimal values of the surge impedances of the transformation lines will then be as follows:

(9) W1= l.5 ohms, I /2:42 ohms, W3=75 ohms.

The ensuing curves for the dependence of the transformation properties upon the frequency correspond almost completely to those in Figure 3.

If the value of W1 is altered a few percent, still better matching conditions may, under certain circumstances, be obtained for one of the sidehands.

If the requirements regarding matching are less severe, or if the width of the band to be transmitted is smaller, then, if circumstances are favorable, an arrangement comprising only two M4 transformation lines may sufiice for the compensation of the load reactance and transformation of the load ohmic resistance. However, these quantities should in such a case not be dimensioned in accordance with Equation 6, for the problem involved in this scheme is to stabilize at zero value throughout the entire band the load reactance having zero value from the outset or transformed to zero, under condition independent of the frequency, and to change at the same time the load ohmic resistance to the desired value. In the present instance, on the contrary, frequency dependence also of the load reactance is supposed, in fact, the same is to be transformed to zero under conditions independent of the frequency. The relationship of the surge impedance of the two M4 transformations is again determined by the known Formula '7'by which the load ohmic resistance, for mean frequency, is transformed to the requisite value. The absolute values of the surge impedances W1 and W2 for the determination of which a further condition may be laid down, may then be determined according to the conditions required in the following fashion:

The rest of the denotations' correspond to those occur-ring in previous equations,

(11) W W1 A The invention is not confined to the matching of an antenna .to an energy feeder line or coaxial cable. On the contrary, it is also useful for inter-coupling any desired complex resistances under conditions free from reflections. The essential feature of the invention is that, contradistinct from what is true of the conventional methods of the earlier art, freedom from reflection is insured for a wide frequency band (for instance, 10 percent detuning) rather than for a single frequency or for a narrow Wave band. Since such a problem arises primarily in the transmission of frequency bands customary in television work from the transmitter to the aerial, the case of coupling an antenna to afeeder line or cable as hereinbefore described has been used as a preferred instance. It is, moreover, immaterial in this connection what particular form has been chosen for the aerial. The numerical examples above cited, for instance, referred exclusively to a M i-antenna fed at its base. If a M2 antenna similarly fed is concerned, then a parallel resonance circuit should be shown in Figure 4 as the equivalent antenna scheme, and in such a case, of course, also the transformation lines must be differently dimensioned.

' I claim:

1. An arrangement adapted to couple a radio frequency load to an energy feeder line without frequency discrimination over a wide band of operating frequencies comprising two or more serially connected impedance transformation lines between said load and said feeder line, each of said transformation lines having a constant surge impedance throughout its length, the length of each line being a multiple, including unity, of a quarter of the wavelength at the midb'and frequency, the surge impedance of the one of said transformation lines nearest said load being so proportioned that the load reactance is transformed to nearly zero under conditions independent of frequency, its effect upon the ohmic resistance being disregarded, while the surge impedance of the remainder of said transformation lines are so proportioned that the load ohmic resistance as transformed by said one transform-ation line is by said remainder of said transformation line transformed to a constant value which is the same as the surge impedance of said feeder line.

2. Arrangement as claimed in claim 1, characterized by two transformation lines each of 7\/2 length, where A is the length of the operating Wave, the energy feeder surge impedance being so chosen that the same is equal to the load ohmic resistance transformed by the two transformation lines.

3. Arrangement as claimed in claim 1 to match a load having a vanishing reactance independent of frequency, with a given energy feeder surge impedance, characterized by the use of two seriated transformation lines between said load and said feeder line, each of said lines being M4 in length, and whose surge impedances are so chosen that ohmic resistance matching prevails and that the load reactance preserves zero value under conditions independent of frequency.

4.:An arrangement claimed in claim 1 to match a load having a vanishing reactance hide pendent of frequency with a given energy feeder surge impedance, characterized by the use of two seriated transformation lines between said load and said feeder line, each of said transformation lines having a length equal to a quarter of the length of the operating wave, the impedance of said quarter wave transformation lines being so chosen that the ohmic resistance of said lead, the impedances of said transformation lines and the impedance of said feeder line form a geometric series.

HANS OTTO ROOSENSTEIN. 

